Suppose we have only Read-write rights to only one host group "Test" where only one host "Host" located.
The Host has linked template from another "Templates" group.

If perform "Unlink and clear" action then we will see success result "Host updated" and the template actually will be unlinked and all objects deleted.
Seems it should not be possible.

Additional issue:
If preform the "Unlink" action then we will see success result "Host updated" but actually the template will not be unlinked.

Connected issue ZBX-3534